已知1+tan/1-tan=3+2根号2,求(sin^2x+根号2sinxcosx-cos^2)/(sin^2+2cos^2)的值
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已知1+tan/1-tan=3+2根号2,求(sin^2x+根号2sinxcosx-cos^2)/(sin^2+2cos^2)的值
已知1+tan/1-tan=3+2根号2,求(sin^2x+根号2sinxcosx-cos^2)/(sin^2+2cos^2)的值
已知1+tan/1-tan=3+2根号2,求(sin^2x+根号2sinxcosx-cos^2)/(sin^2+2cos^2)的值
(1+tanx)/(1-tanx)=3+2根号2
1+tanx = (3+2根号2) - (3+2根号)tanx
2(2+根号2)tanx = 2(根号2+1)
tanx = (根号2+1) / (2+根号2) = 根号2/2
(sin^2x+根号2sinxcosx-cos^2)/(sin^2x+2cos^2x)
分子分母同除以cos^2x:
= ( tan^2x + 根号2 tanx - 1)/(tan^2x+2)
= (1/2 + 1 - 1)/(1/2 + 2)
=(1/2)/(5/2)
=1/5